You are watching: Remote interior angles of a triangle definition
An exterior angle of a triangle is an angle formed by one side of the triangle and the extension of an adjacent side of the triangle.
FACTS: • Every triangle has 6 exterior angles, two at each vertex.• Angles 1 through 6 are exterior angles.• Notice that the “outside” angles that are “vertical” to the angles inside the triangle are NOT called exterior angles of a triangle.
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two non-adjacent interior angles. (Non-adjacent interior angles may also be referred to as remote interior angles.)
FACTS: • An exterior ∠ is equal to the addition of the two Δ angles not right next to it. 140º = 60º + 80º; 120º = 80º + 40º; 100º = 60º + 40º • An exterior angle is supplementary to its adjacent Δ angle. 140º is supp to 40º • The 2 exterior angles at each vertex are = in measure because they are vertical angles. • The exterior angles (taken one at a vertex) always total 360º
Solution: Using the Exterior Angle Theorem 145 = 80 + x x = 65 Now, if you forget the Exterior Angle Theorem, you can still get the answer by noticing that a straight angle has been formed at the vertex of the 145º angle. See Example 2.
Solution: I forgot the Exterior Angle Theorem. The angle adjacent to 145º will form a straight angle along with 145º adding to 180º. That angle is 35º. Now use rule that sum of ∠s in Δ = 180º. 35 + 80 + x = 180 115 + x = 180 x = 65
Find m∠DBC. Solution:∠BDC is an exterior angle for ΔABD. m∠BDC = 35 + 25 m∠BDC = 60º 180 = m∠DBC + 60 + 60 m∠DBC = 60º